Rounding off a single corner of a cube
I think that the "smooth" look of the corner is just a matter of shading (and shaders).

I suggest to simply model it as a cloister vault's corner. Any distortion of the profiles in my opinion would lead to a worse result.



If your boundary profiles are round, you can use the Bevel operator on the two top edge (shortcut Ctrl+B). Then add two (flattened) loopcuts near the corner and Remove Doubles.



Then control the shading (set it to smooth) by marking sharp edges  and adding an Edge split modifier as you can see in the first picture.